Robust Tensor-Based DOA and Polarization Estimation in Conformal Polarization Sensitive Array with Bad Data

Partially impaired sensor arrays pose a significant challenge in accurately estimating signal parameters. The occurrence of bad data is highly probable, resulting in random loss of source information and substantial performance degradation in parameter estimation. In this paper, a tensor variational sparse Bayesian learning (TVSBL) method is proposed for the estimate of direction of arrival (DOA) and polarization parameters jointly based on a conformal polarization sensitive array (CPSA), taking into account scenarios with the partially impaired sensor array. First, a sparse tensor-based received data model is developed for CPSAs that incorporates bad data. Then, a column vector detection method is proposed to diagnose the positions of the impaired sensors. In scenarios involving partially impaired sensor arrays, a low-rank matrix completion method is employed to recover the random loss of signal information. Finally, variational sparse Bayesian learning (VSBL) and minimum eigenvector methods are utilized sequentially to obtain the DOA and polarization parameters estimation, successively. Furthermore, the Cramér-Rao bound is given for the proposed method. Simulation results validated the effectiveness of the proposed method.

Adaptive Tensor-Based Feature Extraction for Pupil Segmentation in Cataract Surgery

Cataract surgery remains the only definitive treatment for visually significant cataracts, which are a major cause of preventable blindness worldwide. Successful performance of cataract surgery relies on stable dilation of the pupil. Automated pupil segmentation from surgical videos can assist surgeons in detecting risk factors for pupillary instability prior to the development of surgical complications. However, surgical illumination variations, surgical instrument obstruction, and lens material hydration during cataract surgery can limit pupil segmentation accuracy. To address these problems, we propose a novel method named adaptive wavelet tensor feature extraction (AWTFE). AWTFE is designed to enhance the accuracy of deep learning-powered pupil recognition systems. First, we represent the correlations among spatial information, color channels, and wavelet subbands by constructing a third-order tensor. We then utilize higher-order singular value decomposition to eliminate redundant information adaptively and estimate pupil feature information. We evaluated the proposed method by conducting experiments with state-of-the-art deep learning segmentation models on our BigCat dataset consisting of 5,700 annotated intraoperative images from 190 cataract surgeries and a public CaDIS dataset. The experimental results reveal that the AWTFE method effectively identifies features relevant to the pupil region and improved the overall performance of segmentation models by up to 2.26% (BigCat) and 3.31% (CaDIS). Incorporation of the AWTFE method led to statistically significant improvements in segmentation performance (P < 1.29  ×  10-10 for each model) and yielded the highest-performing model overall (Dice coefficients of 94.74% and 96.71% for the BigCat and CaDIS datasets, respectively). In performance comparisons, the AWTFE consistently outperformed other feature extraction methods in enhancing model performance. In addition, the proposed AWTFE method significantly improved pupil recognition performance by up to 2.87% in particularly challenging phases of cataract surgery.

ETucker: a constrained tensor decomposition for single trial ERP extraction

Objective.In this paper, we propose a new tensor decomposition to extract event-related potentials (ERP) by adding a physiologically meaningful constraint to the Tucker decomposition.Approach.We analyze the performance of the proposed model and compare it with Tucker decomposition by synthesizing a dataset. The simulated dataset is generated using a 12th-order autoregressive model in combination with independent component analysis (ICA) on real no-task electroencephalogram (EEG) recordings. The dataset is manipulated to contain the P300 ERP component and to cover different SNR conditions, ranging from 0 to -30 dB, to simulate the presence of the P300 component in extremely noisy recordings. Furthermore, in order to assess the practicality of the proposed methodology in real-world scenarios, we utilized the brain-computer interface (BCI) competition III-dataset II.Main results.Our primary results demonstrate the superior performance of our approach compared to conventional methods commonly employed for single-trial estimation. Additionally, our method outperformed both Tucker decomposition and non-negative Tucker decomposition in the synthesized dataset. Furthermore, the results obtained from real-world data exhibited meaningful performance and provided insightful interpretations for the extracted P300 component.Significance.The findings suggest that the proposed decomposition is eminently capable of extracting the target P300 component's waveform, including latency and amplitude as well as its spatial location, using single-trial EEG recordings.

Change-Point Detection for Multi-Way Tensor-Based Frameworks

Graph-based change-point detection methods are often applied due to their advantages for using high-dimensional data. Most applications focus on extracting effective information of objects while ignoring their main features. However, in some applications, one may be interested in detecting objects with different features, such as color. Therefore, we propose a general graph-based change-point detection method under the multi-way tensor framework, aimed at detecting objects with different features that change in the distribution of one or more slices. Furthermore, considering that recorded tensor sequences may be vulnerable to natural disturbances, such as lighting in images or videos, we propose an improved method incorporating histogram equalization techniques to improve detection efficiency. Finally, through simulations and real data analysis, we show that the proposed methods achieve higher efficiency in detecting change-points.

Torch-eCpG: A fast and scalable eQTM mapper for thousands of molecular phenotypes with graphical processing units

Background

Gene expression may be regulated by the DNA methylation of regulatory elements in cis, distal, and trans regions. One method to evaluate the relationship between DNA methylation and gene expression is the mapping of expression quantitative trait methylation (eQTM) loci (also called expression associated CpG loci, eCpG). However, no open-source tools are available to provide eQTM mapping. In addition, eQTM mapping can involve a large number of comparisons which may prevent the analyses due to limitations of computational resources. Here, we describe Torch-eCpG, an open-source tool to perform eQTM mapping that includes an optimized implementation that can use the graphical processing unit (GPU) to reduce runtime.

Results

We demonstrate the analyses using the tool are reproducible, up to 18x faster using the GPU, and scale linearly with increasing methylation loci.

Conclusions

Torch-eCpG is a fast, reliable, and scalable tool to perform eQTM mapping. Source code for Torch-eCpG is available at https://github.com/kordk/torch-ecpg.

TensorView for MATLAB: Visualizing tensors with Euler angle decoding

TensorView for MATLAB is a GUI-based visualization tool for depicting second-rank Cartesian tensors as surfaces on three-dimensional molecular models. Both ellipsoid and ovaloid tensor display formats are supported, and the software allows for easy conversion of Euler angles from common rotation schemes (active, passive, ZXZ, and ZYZ conventions) with visual feedback. In addition, the software displays all four orientation-equivalent Euler angle solutions for the placement of a single tensor in the molecular frame and can report relative orientations of two tensors with all 16 orientation-equivalent Euler angle sets that relate them. The salient relations are derived and illustrated through several examples. TensorView for MATLAB expands and complements the earlier implementation of TensorView within the Mathematica programming environment and can be run without a MATLAB license. TensorView for MATLAB is available through github at https://github.com/LeoSvenningsson/TensorViewforMatlab, and can also be accessed directly via the NMRbox resource.

Single-cell transcriptome analysis illuminating the characteristics of species-specific innate immune responses against viral infections

BACKGROUND

Bats harbor various viruses without severe symptoms and act as their natural reservoirs. The tolerance of bats against viral infections is assumed to originate from the uniqueness of their immune system. However, how immune responses vary between primates and bats remains unclear. Here, we characterized differences in the immune responses by peripheral blood mononuclear cells to various pathogenic stimuli between primates (humans, chimpanzees, and macaques) and bats (Egyptian fruit bats) using single-cell RNA sequencing.

RESULTS

We show that the induction patterns of key cytosolic DNA/RNA sensors and antiviral genes differed between primates and bats. A novel subset of monocytes induced by pathogenic stimuli specifically in bats was identified. Furthermore, bats robustly respond to DNA virus infection even though major DNA sensors are dampened in bats.

CONCLUSIONS

Overall, our data suggest that immune responses are substantially different between primates and bats, presumably underlying the difference in viral pathogenicity among the mammalian species tested.

Adaptive granularity in tensors: A quest for interpretable structure

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus, the utility of such tensors is low, in terms of the amount of interpretable and exploitable structure that one can extract from them. In this paper, we introduce the problem of finding a tensor of adaptive aggregated granularity that can be decomposed to reveal meaningful latent concepts (structures) from datasets that, in their original form, are not amenable to tensor analysis. Such datasets fall under the broad category of sparse point processes that evolve over space and/or time. To the best of our knowledge, this is the first work that explores adaptive granularity aggregation in tensors. Furthermore, we formally define the problem and discuss different definitions of "good structure" that are in practice and show that the optimal solution is of prohibitive combinatorial complexity. Subsequently, we propose an efficient and effective greedy algorithm called ICEBREAKER, which follows a number of intuitive decision criteria that locally maximize the "goodness of structure," resulting in high-quality tensors. We evaluate our method on synthetic, semi-synthetic, and real datasets. In all the cases, our proposed method constructs tensors that have a very high structure quality.

Finger movement and coactivation predicted from intracranial brain activity using extended block-term tensor regression

Objective.We introduce extended Block-Term Tensor Regression (eBTTR), a novel regression method designed to account for the multilinear nature of human intracranial finger movement recordings.Approach.The proposed method relies on recursive Tucker decomposition combined with automatic component extraction.Main results.eBTTR outperforms state-of-the-art regression approaches, including multilinear and deep learning ones, in accurately predicting finger trajectories as well as unintentional finger coactivations.Significance.eBTTR rivals state-of-the-art approaches while being less computationally expensive which is an advantage when intracranial electrodes are implanted acutely, as part of the patient's presurgical workup, limiting time for decoder development and testing.

Tensor-Based Multi-Modality Feature Selection and Regression for Alzheimer's Disease Diagnosis

The assessment of Alzheimer's Disease (AD) and Mild Cognitive Impairment (MCI) associated with brain changes remains a challenging task. Recent studies have demonstrated that combination of multi-modality imaging techniques can better reflect pathological characteristics and contribute to more accurate diagnosis of AD and MCI. In this paper, we propose a novel tensor-based multi-modality feature selection and regression method for diagnosis and biomarker identification of AD and MCI from normal controls. Specifically, we leverage the tensor structure to exploit high-level correlation information inherent in the multi-modality data, and investigate tensor-level sparsity in the multilinear regression model. We present the practical advantages of our method for the analysis of ADNI data using three imaging modalities (VBM-MRI, FDG-PET and AV45-PET) with clinical parameters of disease severity and cognitive scores. The experimental results demonstrate the superior performance of our proposed method against the state-of-the-art for the disease diagnosis and the identification of disease-specific regions and modality-related differences. The code for this work is publicly available at https://github.com/junfish/BIOS22.

Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM

Recently, the joint estimation for time delay (TD) and direction of arrival (DOA) has suffered from the high complexity of processing multi-dimensional signal models and the ineffectiveness of correlated/coherent signals. In order to improve this situation, a joint estimation method using orthogonal frequency division multiplexing (OFDM) and a uniform planar array composed of reconfigurable intelligent surface (RIS) is proposed. First, the time-domain coding function of the RIS is combined with the multi-carrier characteristic of the OFDM signal to construct the coded channel frequency response in tensor form. Then, the coded channel frequency response covariance matrix is decomposed by CANDECOMP/PARAFAC (CPD) to separate the signal subspaces of TD and DOA. Finally, we perform a one-dimensional (1D) spectral search for TD values and a two-dimensional (2D) spectral search for DOA values. Compared to previous efforts, this algorithm not only enhances the adaptability of coherent signals, but also greatly decreases the complexity. Simulation results indicate the robustness and effectiveness for the proposed algorithm in independent, coherent, and mixed multipath environments and low signal-to-noise ratio (SNR) conditions.

Multi-Modal Image Fusion Based on Matrix Product State of Tensor

Multi-modal image fusion integrates different images of the same scene collected by different sensors into one image, making the fused image recognizable by the computer and perceived by human vision easily. The traditional tensor decomposition is an approximate decomposition method and has been applied to image fusion. In this way, the image details may be lost in the process of fusion image reconstruction. To preserve the fine information of the images, an image fusion method based on tensor matrix product decomposition is proposed to fuse multi-modal images in this article. First, each source image is initialized into a separate third-order tensor. Then, the tensor is decomposed into a matrix product form by using singular value decomposition (SVD), and the Sigmoid function is used to fuse the features extracted in the decomposition process. Finally, the fused image is reconstructed by multiplying all the fused tensor components. Since the algorithm is based on a series of singular value decomposition, a stable closed solution can be obtained and the calculation is also simple. The experimental results show that the fusion image quality obtained by this algorithm is superior to other algorithms in both objective evaluation metrics and subjective evaluation.

A Multi-Modal Fusion Method Based on Higher-Order Orthogonal Iteration Decomposition

Multi-modal fusion can achieve better predictions through the amalgamation of information from different modalities. To improve the performance of accuracy, a method based on Higher-order Orthogonal Iteration Decomposition and Projection (HOIDP) is proposed, in the fusion process, higher-order orthogonal iteration decomposition algorithm and factor matrix projection are used to remove redundant information duplicated inter-modal and produce fewer parameters with minimal information loss. The performance of the proposed method is verified by three different multi-modal datasets. The numerical results validate the accuracy of the performance of the proposed method having 0.4% to 4% improvement in sentiment analysis, 0.3% to 8% improvement in personality trait recognition, and 0.2% to 25% improvement in emotion recognition at three different multi-modal datasets compared with other 5 methods.

Physical Activity Recognition Based on a Parallel Approach for an Ensemble of Machine Learning and Deep Learning Classifiers

Human activity recognition (HAR) by wearable sensor devices embedded in the Internet of things (IOT) can play a significant role in remote health monitoring and emergency notification to provide healthcare of higher standards. The purpose of this study is to investigate a human activity recognition method of accrued decision accuracy and speed of execution to be applicable in healthcare. This method classifies wearable sensor acceleration time series data of human movement using an efficient classifier combination of feature engineering-based and feature learning-based data representation. Leave-one-subject-out cross-validation of the method with data acquired from 44 subjects wearing a single waist-worn accelerometer on a smart textile, and engaged in a variety of 10 activities, yielded an average recognition rate of 90%, performing significantly better than individual classifiers. The method easily accommodates functional and computational parallelization to bring execution time significantly down.

Tensor-tensor algebra for optimal representation and compression of multiway data

With the advent of machine learning and its overarching pervasiveness it is imperative to devise ways to represent large datasets efficiently while distilling intrinsic features necessary for subsequent analysis. The primary workhorse used in data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. A primary goal in this study is to show that high-dimensional datasets are more compressible when treated as tensors (i.e., multiway arrays) and compressed via tensor-SVDs under the tensor-tensor product constructs and its generalizations. We begin by proving Eckart-Young optimality results for families of tensor-SVDs under two different truncation strategies. Since such optimality properties can be proven in both matrix and tensor-based algebras, a fundamental question arises: Does the tensor construct subsume the matrix construct in terms of representation efficiency? The answer is positive, as proven by showing that a tensor-tensor representation of an equal dimensional spanning space can be superior to its matrix counterpart. We then use these optimality results to investigate how the compressed representation provided by the truncated tensor SVD is related both theoretically and empirically to its two closest tensor-based analogs, the truncated high-order SVD and the truncated tensor-train SVD.

Detecting Group Anomalies in Tera-Scale Multi-Aspect Data via Dense-Subtensor Mining

How can we detect fraudulent lockstep behavior in large-scale multi-aspect data (i.e., tensors)? Can we detect it when data are too large to fit in memory or even on a disk? Past studies have shown that dense subtensors in real-world tensors (e.g., social media, Wikipedia, TCP dumps, etc.) signal anomalous or fraudulent behavior such as retweet boosting, bot activities, and network attacks. Thus, various approaches, including tensor decomposition and search, have been proposed for detecting dense subtensors rapidly and accurately. However, existing methods suffer from low accuracy, or they assume that tensors are small enough to fit in main memory, which is unrealistic in many real-world applications such as social media and web. To overcome these limitations, we propose D-Cube, a disk-based dense-subtensor detection method, which also can run in a distributed manner across multiple machines. Compared to state-of-the-art methods, D-Cube is (1) Memory Efficient: requires up to 1,561× less memory and handles 1,000× larger data (2.6TB), (2) Fast: up to 7× faster due to its near-linear scalability, (3) Provably Accurate: gives a guarantee on the densities of the detected subtensors, and (4) Effective: spotted network attacks from TCP dumps and synchronized behavior in rating data most accurately.

Age-Related Differences in White Matter: Understanding Tensor-Based Results Using Fixel-Based Analysis

Aging is associated with widespread alterations in cerebral white matter (WM). Most prior studies of age differences in WM have used diffusion tensor imaging (DTI), but typical DTI metrics (e.g., fractional anisotropy; FA) can reflect multiple neurobiological features, making interpretation challenging. Here, we used fixel-based analysis (FBA) to investigate age-related WM differences observed using DTI in a sample of 45 older and 25 younger healthy adults. Age-related FA differences were widespread but were strongly associated with differences in multi-fiber complexity (CX), suggesting that they reflected differences in crossing fibers in addition to structural differences in individual fiber segments. FBA also revealed a frontolimbic locus of age-related effects and provided insights into distinct microstructural changes underlying them. Specifically, age differences in fiber density were prominent in fornix, bilateral anterior internal capsule, forceps minor, body of the corpus callosum, and corticospinal tract, while age differences in fiber cross section were largest in cingulum bundle and forceps minor. These results provide novel insights into specific structural differences underlying major WM differences associated with aging.

A machine learning cardiac magnetic resonance approach to extract disease features and automate pulmonary arterial hypertension diagnosis

AIMS

Pulmonary arterial hypertension (PAH) is a progressive condition with high mortality. Quantitative cardiovascular magnetic resonance (CMR) imaging metrics in PAH target individual cardiac structures and have diagnostic and prognostic utility but are challenging to acquire. The primary aim of this study was to develop and test a tensor-based machine learning approach to holistically identify diagnostic features in PAH using CMR, and secondarily, visualize and interpret key discriminative features associated with PAH.

METHODS AND RESULTS

Consecutive treatment naive patients with PAH or no evidence of pulmonary hypertension (PH), undergoing CMR and right heart catheterization within 48 h, were identified from the ASPIRE registry. A tensor-based machine learning approach, multilinear subspace learning, was developed and the diagnostic accuracy of this approach was compared with standard CMR measurements. Two hundred and twenty patients were identified: 150 with PAH and 70 with no PH. The diagnostic accuracy of the approach was high as assessed by area under the curve at receiver operating characteristic analysis (P < 0.001): 0.92 for PAH, slightly higher than standard CMR metrics. Moreover, establishing the diagnosis using the approach was less time-consuming, being achieved within 10 s. Learnt features were visualized in feature maps with correspondence to cardiac phases, confirming known and also identifying potentially new diagnostic features in PAH.

CONCLUSION

A tensor-based machine learning approach has been developed and applied to CMR. High diagnostic accuracy has been shown for PAH diagnosis and new learnt features were visualized with diagnostic potential.

Tensor decomposition for infectious disease incidence data

Many demographic and ecological processes generate seasonal and other periodicities. Seasonality in infectious disease transmission can result from climatic forces such as temperature and humidity; variation in contact rates as a result of migration or school calendar; or temporary surges in birth rates. Seasonal drivers of acute immunizing infections can also drive longer-term fluctuations.Tensor decomposition has been used in many disciplines to uncover dominant trends in multi-dimensional data. We introduce tensors as a novel method for decomposing oscillatory infectious disease time series.We illustrate the reliability of the method by applying it to simulated data. We then present decompositions of measles data from England and Wales. This paper leverages simulations as well as much-studied data to illustrate the power of tensor decomposition to uncover dominant epidemic signals as well as variation in space and time. We then use tensor decomposition to uncover new findings and demonstrate the potential power of the method for disease incidence data. In particular, we are able to distinguish between annual and biennial signals across locations and shifts in these signals over time.Tensor decomposition is able to isolate variation in disease seasonality as a result of variation in demographic rates. The method allows us to discern variation in the strength of such signals by space and population size. Tensors provide an opportunity for a concise approach to uncovering heterogeneity in disease transmission across space and time in large datasets.

A Tensor-Based Framework for rs-fMRI Classification and Functional Connectivity Construction

Recently, machine learning methods have gained lots of attention from researchers seeking to analyze brain images such as Resting-State Functional Magnetic Resonance Imaging (rs-fMRI) to obtain a deeper understanding of the brain and such related diseases, for example, Alzheimer's disease. Finding the common patterns caused by a brain disorder through analysis of the functional connectivity (FC) network along with discriminating brain diseases from normal controls have long been the two principal goals in studying rs-fMRI data. The majority of FC extraction methods calculate the FC matrix for each subject and then use simple techniques to combine them and obtain a general FC matrix. In addition, the state-of-the-art classification techniques for finding subjects with brain disorders also rely on calculating an FC for each subject, vectorizing, and feeding them to the classifier. Considering these problems and based on multi-dimensional nature of the data, we have come up with a novel tensor framework in which a general FC matrix is obtained without the need to construct an FC matrix for each sample. This framework also allows us to reduce the dimensionality and create a novel discriminant function that rather than using FCs works directly with each sample, avoids vectorization in any step, and uses the test data in the training process without forcing any prior knowledge of its label into the classifier. Extensive experiments using the ADNI dataset demonstrate that our proposed framework effectively boosts the fMRI classification performance and reveals novel connectivity patterns in Alzheimer's disease at its early stages.

A Novel Computational Approach for Identifying Essential Proteins From Multiplex Biological Networks

The identification of essential proteins can help in understanding the minimum requirements for cell survival and development. Ever-increasing amounts of high-throughput data provide us with opportunities to detect essential proteins from protein interaction networks (PINs). Existing network-based approaches are limited by the poor quality of the underlying PIN data, which exhibits high rates of false positive and false negative results. To overcome this problem, researchers have focused on the prediction of essential proteins by combining PINs with other biological data, which has led to the emergence of various interactions between proteins. It remains challenging, however, to use aggregated multiplex interactions within a single analysis framework to identify essential proteins. In this study, we created a multiplex biological network (MON) by initially integrating PINs, protein domains, and gene expression profiles. Next, we proposed a new approach to discover essential proteins by extending the random walk with restart algorithm to the tensor, which provides a data model representation of the MON. In contrast to existing approaches, the proposed MON approach considers for the importance of nodes and the different types of interactions between proteins during the iteration. MON was implemented to identify essential proteins within two yeast PINs. Our comprehensive experimental results demonstrated that MON outperformed 11 other state-of-the-art approaches in terms of precision-recall curve, jackknife curve, and other criteria.

Coupled CP Decomposition of Simultaneous MEG-EEG Signals for Differentiating Oscillators During Photic Driving

Magnetoencephalography (MEG) and electroencephalography (EEG) are contemporary methods to investigate the function and organization of the brain. Simultaneously acquired MEG-EEG data are inherently multi-dimensional and exhibit coupling. This study uses a coupled tensor decomposition to extract the signal sources from MEG-EEG during intermittent photic stimulation (IPS). We employ the Coupled Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization (C-SECSI). After comparing its performance with alternative methods using simulated benchmark data, we apply it to MEG-EEG recordings of 12 participants during IPS with fractions of the individual alpha frequency between 0.4 and 1.3. In the benchmark tests, C-SECSI is more accurate than SECSI and alternative methods, especially in ill-conditioned scenarios, e.g., involving collinear factors or noise sources with different variances. The component field-maps allow us to separate physiologically meaningful oscillations of visually evoked brain activity from background signals. The frequency signatures of the components identify either an entrainment to the respective stimulation frequency or its first harmonic, or an oscillation in the individual alpha band or theta band. In the group analysis of both, MEG and EEG data, we observe a reciprocal relationship between alpha and theta band oscillations. The coupled tensor decomposition using C-SECSI is a robust, powerful method for the extraction of physiologically meaningful sources from multidimensional biomedical data. Unsupervised signal source extraction is an essential solution for rendering advanced multi-modal signal acquisition technology accessible to clinical diagnostics, pre-surgical planning, and brain computer interface applications.

A framework for second-order eigenvector centralities and clustering coefficients

We propose and analyse a general tensor-based framework for incorporating second-order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods and recently proposed cases from the literature, but we also identify many interesting extensions. In particular, we define a mutually reinforcing (spectral) version of the classical clustering coefficient. The underlying object of study is a constrained nonlinear eigenvalue problem associated with a cubic tensor. Using recent results from nonlinear Perron-Frobenius theory, we establish existence and uniqueness under appropriate conditions, and show that the new spectral measures can be computed efficiently with a nonlinear power method. To illustrate the added value of the new formulation, we analyse the measures on a class of synthetic networks. We also give computational results on centrality and link prediction for real-world networks.

TensorView: A software tool for displaying NMR tensors

The representation of nuclear magnetic resonance (NMR) tensors as surfaces on three-dimensional molecular models is an information-rich presentation that highlights the geometric relationship between tensor principal components and the underlying molecular and electronic structure. Here, we describe a new computational tool, TensorView, for depicting NMR tensors on the molecular framework. This package makes use of the graphical interface and built-in molecular display functionality present within the Mathematica programming environment and is robust for displaying tensor properties from a broad range of commercial and user-specific computational chemistry packages. Two mathematical forms for representing tensor interaction surfaces are presented, the popular ellipsoidal construct and the more technically correct "ovaloid" form. Examples are provided for chemical shielding and shift tensors, dipole-dipole and quadrupolar couplings, and atomic anisotropic displacement parameters (thermal ellipsoids) derived from NMR crystallography.

A video watermark algorithm based on tensor decomposition

Since most of the previous video watermark algorithms regard a video as a series of consecutive images, the embedding and extraction of watermark are performed on these images, and the correlation and redundancy among frames of a video are not considered. Such algorithms are weak in protecting against frame attacks. In order to improve the robustness, we take into consideration the correlation and redundancy among the frames of a video to propose a blind video watermark algorithm based on tensor decomposition. First, a grayscale video is represented as a 3-order tensor, and the core tensor is obtained by tensor decomposition. Second, the watermark embedding position is selected based on the stability of the maximum value in the core tensor because the core tensor represents the main energy of a video. Then, the watermark is embedded by quantifying the maximum value in the core tensor. Finally, the watermark is uniformly distributed across frames of a video by inverse tensor decomposition. The experiments show that our algorithm based on tensor decomposition has better imperceptibility and robustness against common video attacks.

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Dynamic cerebral perfusion computed tomography (DCPCT) has the ability to evaluate the hemodynamic information throughout the brain. However, due to multiple 3-D image volume acquisitions protocol, DCPCT scanning imposes high radiation dose on the patients with growing concerns. To address this issue, in this paper, based on the robust principal component analysis (RPCA, or equivalently the low-rank and sparsity decomposition) model and the DCPCT imaging procedure, we propose a new DCPCT image reconstruction algorithm to improve low-dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basis-representation tensor sparsity regularization, for measuring low-rankness extent of a tensor. For simplicity, the first proposed model is termed tensor-based RPCA (T-RPCA). Specifically, the T-RPCA model views the DCPCT sequential images as a mixture of low-rank, sparse, and noise components to describe the maximum temporal coherence of spatial structure among phases in a tensor framework intrinsically. Moreover, the low-rank component corresponds to the "background" part with spatial-temporal correlations, e.g., static anatomical contribution, which is stationary over time about structure, and the sparse component represents the time-varying component with spatial-temporal continuity, e.g., dynamic perfusion enhanced information, which is approximately sparse over time. Furthermore, an improved nonlocal patch-based T-RPCA (NL-T-RPCA) model which describes the 3-D block groups of the "background" in a tensor is also proposed. The NL-T-RPCA model utilizes the intrinsic characteristics underlying the DCPCT images, i.e., nonlocal self-similarity and global correlation. Two efficient algorithms using alternating direction method of multipliers are developed to solve the proposed T-RPCA and NL-T-RPCA models, respectively. Extensive experiments with a digital brain perfusion phantom, preclinical monkey data, and clinical patient data clearly demonstrate that the two proposed models can achieve more gains than the existing popular algorithms in terms of both quantitative and visual quality evaluations from low-dose acquisitions, especially as low as 20 mAs.

Tensor estimation for double-pulsed diffusional kurtosis imaging

Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented.

Full-State Controls of Terahertz Waves Using Tensor Coding Metasurfaces

Coding metasurfaces allow us to study metamaterials from a fully digital perspective, enabling many exotic functionalities, such as anomalous reflections, broadband diffusions, and polarization conversion. Here, we propose a tensor coding metasurface at terahertz (THz) frequency that could take full-state controls of an electromagnetic wave in terms of its polarization state, phase and amplitude distributions, and wave-vector mode. Owing to the off-diagonal elements that dominant in the reflection matrix, each coding particle could reflect the normally incident wave to its cross-polarization with controllable phases, resulting in different coding digits. A 3-bit tensor coding metasurface with three coding sequences is taken as an example to show its full-state controls in reflecting a normally incident THz beam to anomalous directions with cross-polarizations and making a spatially propagating wave (PW) to surface wave (SW) conversion at the THz frequency. We show that the proposed PW-SW convertor based on the tensor coding metasurface supports both x- and y-polarized normal incidences, producing cross-polarized transverse-magnetic and transverse-electric modes of THz SWs, respectively.

Evaluating kurtosis-based diffusion MRI tissue models for white matter with fiber ball imaging

In order to quantify well-defined microstructural properties of brain tissue from diffusion MRI (dMRI) data, tissue models are typically employed that relate biological features, such as cell morphology and cell membrane permeability, to the diffusion dynamics. A variety of such models have been proposed for white matter, and their validation is a topic of active interest. In this paper, three different tissue models are tested by comparing their predictions for a specific microstructural parameter to a value measured independently with a recently proposed dMRI method known as fiber ball imaging (FBI). The three tissue models are all constructed with the diffusion and kurtosis tensors, and they are hence compatible with diffusional kurtosis imaging. Nevertheless, the models differ significantly in their details and predictions. For voxels with fractional anisotropies (FAs) exceeding 0.5, all three are reasonably consistent with FBI. However, for lower FA values, one of these, called the white matter tract integrity (WMTI) model, is found to be in much better accord with FBI than the other two, suggesting that the WMTI model has a broader range of applicability.

Diffusion MRI in the heart

Diffusion MRI provides unique information on the structure, organization, and integrity of the myocardium without the need for exogenous contrast agents. Diffusion MRI in the heart, however, has proven technically challenging because of the intrinsic non-rigid deformation during the cardiac cycle, displacement of the myocardium due to respiratory motion, signal inhomogeneity within the thorax, and short transverse relaxation times. Recently developed accelerated diffusion-weighted MR acquisition sequences combined with advanced post-processing techniques have improved the accuracy and efficiency of diffusion MRI in the myocardium. In this review, we describe the solutions and approaches that have been developed to enable diffusion MRI of the heart in vivo, including a dual-gated stimulated echo approach, a velocity- (M1 ) or an acceleration- (M2 ) compensated pulsed gradient spin echo approach, and the use of principal component analysis filtering. The structure of the myocardium and the application of these techniques in ischemic heart disease are also briefly reviewed. The advent of clinical MR systems with stronger gradients will likely facilitate the translation of cardiac diffusion MRI into clinical use. The addition of diffusion MRI to the well-established set of cardiovascular imaging techniques should lead to new and complementary approaches for the diagnosis and evaluation of patients with heart disease. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

Effective potential for magnetic resonance measurements of restricted diffusion

The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

Postoperative Knee Flexion Angle Is Affected by Lateral Laxity in Cruciate-Retaining Total Knee Arthroplasty

BACKGROUND

Although many studies have reported that postoperative knee flexion is influenced by preoperative conditions, the factors which affect postoperative knee flexion have not been fully elucidated. We tried to investigate the influence of intraoperative soft tissue balance on postoperative knee flexion angle after cruciate-retaining (CR) total knee arthroplasty (TKA) using a navigation and an offset-type tensor.

METHODS

We retrospectively analyzed 55 patients with osteoarthritis who underwent TKA using e.motion-CR (B. Braun Aesculap, Germany) whose knee flexion angle could be measured at 2 years after operation. The exclusion criteria included valgus deformity, severe bony defect, infection, and bilateral TKA. Intraoperative varus ligament balance and joint component gap were measured with the navigation (Orthopilot 4.2; B. Braun Aesculap) while applying 40-lb joint distraction force at 0° to 120° of knee flexion using an offset-type tensor. Correlations between the soft tissue parameters and postoperative knee flexion angle were analyzed using simple linear regression models.

RESULTS

Varus ligament balance at 90° of flexion (R = 0.56; P < .001) and lateral compartment gap at 90° of flexion (R = 0.51; P < .001) were positively correlated with postoperative knee flexion angle. In addition, as with past studies, joint component gap at 90° of flexion (R = 0.30; P < .05) and preoperative knee flexion angle (R = 0.63; P < .001) were correlated with postoperative knee flexion angle.

CONCLUSION

Lateral laxity as well as joint component gap at 90° of flexion is one of the most important factors affecting postoperative knee flexion angle in CR-TKA.

Functional Neuroimaging: Fundamental Principles and Clinical Applications

Functional imaging modalities, such as functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI), are rapidly changing the scope and practice of neuroradiology. While these modalities have long been used in research, they are increasingly being used in clinical practice to enable reliable identification of eloquent cortex and white matter tracts in order to guide treatment planning and to serve as a diagnostic supplement when traditional imaging fails. An understanding of the scientific principles underlying fMRI and DTI is necessary in current radiological practice. fMRI relies on a compensatory hemodynamic response seen in cortical activation and the intrinsic discrepant magnetic properties of deoxy- and oxyhemoglobin. Neuronal activity can be indirectly visualized based on a hemodynamic response, termed neurovascular coupling. fMRI demonstrates utility in identifying areas of cortical activation (i.e., task-based activation) and in discerning areas of neuronal connectivity when used during the resting state, termed resting state fMRI. While fMRI is limited to visualization of gray matter, DTI permits visualization of white matter tracts through diffusion restriction along different axes. We will discuss the physical, statistical and physiological principles underlying these functional imaging modalities and explore new promising clinical applications.

Tensor-based Multi-view Feature Selection with Applications to Brain Diseases

In the era of big data, we can easily access information from multiple views which may be obtained from different sources or feature subsets. Generally, different views provide complementary information for learning tasks. Thus, multi-view learning can facilitate the learning process and is prevalent in a wide range of application domains. For example, in medical science, measurements from a series of medical examinations are documented for each subject, including clinical, imaging, immunologic, serologic and cognitive measures which are obtained from multiple sources. Specifically, for brain diagnosis, we can have different quantitative analysis which can be seen as different feature subsets of a subject. It is desirable to combine all these features in an effective way for disease diagnosis. However, some measurements from less relevant medical examinations can introduce irrelevant information which can even be exaggerated after view combinations. Feature selection should therefore be incorporated in the process of multi-view learning. In this paper, we explore tensor product to bring different views together in a joint space, and present a dual method of tensor-based multi-view feature selection (dual-Tmfs) based on the idea of support vector machine recursive feature elimination. Experiments conducted on datasets derived from neurological disorder demonstrate the features selected by our proposed method yield better classification performance and are relevant to disease diagnosis.

HIERARCHICAL ARRAY PRIORS FOR ANOVA DECOMPOSITIONS OF CROSS-CLASSIFIED DATA

ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matrices and arrays that share various index sets defined by the factor levels. For many types of categorical factors, it is plausible that an ANOVA decomposition exhibits some consistency across orders of effects, in that the levels of a factor that have similar main-effect coefficients may also have similar coefficients in higher-order interaction terms. In such a case, estimation of the higher-order interactions should be improved by borrowing information from the main effects and lower-order interactions. To take advantage of such patterns, this article introduces a class of hierarchical prior distributions for collections of interaction arrays that can adapt to the presence of such interactions. These prior distributions are based on a type of array-variate normal distribution, for which a covariance matrix for each factor is estimated. This prior is able to adapt to potential similarities among the levels of a factor, and incorporate any such information into the estimation of the effects in which the factor appears. In the presence of such similarities, this prior is able to borrow information from well-estimated main effects and lower-order interactions to assist in the estimation of higher-order terms for which data information is limited.

Double-pulsed diffusional kurtosis imaging

Diffusional kurtosis imaging (DKI) is extended to double-pulsed-field-gradient (d-PFG) diffusion MRI sequences. This gives a practical approach for acquiring and analyzing d-PFG data. In particular, the leading d-PFG effects, beyond what conventional single-pulsed field gradient (s-PFG) provides, are interpreted in terms of the kurtosis for a diffusion displacement probability density function (dPDF) in a six-dimensional (6D) space. The 6D diffusional kurtosis encodes the unique information provided by d-PFG sequences up to second order in the b-value. This observation leads to a compact expression for the signal magnitude, and it suggests novel data acquisition and analysis methods. Double-pulsed DKI (DP-DKI) is demonstrated for in vivo mouse brain with d-PFG data obtained at 7 T. Copyright © 2014 John Wiley & Sons, Ltd.

Leading non-Gaussian corrections for diffusion orientation distribution function

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common.

A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies

Different from the single-energy CT (SECT), multi-energy CT (MECT) acquires projection data at different energy spectra, which makes that the MECT has more sparsity among the data of separate energy and over energy. In order to maximize utilization of all these sparse characteristics, this paper proposed a new tensor PRISM model to consistently treat a priori knowledge of the low rank, intensity and sparsity with the higher-dimensional tensor technique. The priori knowledge of low rank corresponds to the stationary background and similarity over the energy, and the intensity and sparsity represents the rest of image features at single energy. Then, the regularization and convex minimization problem was solved by tensor unfolding and an extended tensor-based split-Bregman algorithm. Different from the previous PRISM algorithm, the new algorithm mixed and treated different constraints consistently. Numerical experiments have shown that our tensor PRISM approach performs much better than the popular l1 regularization algorithm in terms of image quality for MECT.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

Development of white matter and reading skills

White matter tissue properties are highly correlated with reading proficiency; we would like to have a model that relates the dynamics of an individual's white matter development to their acquisition of skilled reading. The development of cerebral white matter involves multiple biological processes, and the balance between these processes differs between individuals. Cross-sectional measures of white matter mask the interplay between these processes and their connection to an individual's cognitive development. Hence, we performed a longitudinal study to measure white-matter development (diffusion-weighted imaging) and reading development (behavioral testing) in individual children (age 7-15 y). The pattern of white-matter development differed significantly among children. In the left arcuate and left inferior longitudinal fasciculus, children with above-average reading skills initially had low fractional anisotropy (FA) that increased over the 3-y period, whereas children with below-average reading skills had higher initial FA that declined over time. We describe a dual-process model of white matter development comprising biological processes with opposing effects on FA, such as axonal myelination and pruning, to explain the pattern of results.

How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 Collapse

Key Words

• high-angular resolution diffusion imaging
• anisotropic scalar
• generalized fractional anisotropy
• tensor
• signal-to-noise ratio
• kullback-leibler divergence

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MESH Headings

• Algorithms
• Anisotropy
• Computer Simulation
• Corpus Callosum/physiology
• Diffusion
• Diffusion Magnetic Resonance Imaging/methods
• Female
• Humans
• Imaging, Three-Dimensional/methods
• Male
• Models, Neurological
• Young Adult

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Grants

• EB007813 NIBIB NIH HHS
• R01 EB007813 NIBIB NIH HHS
• AG020098 NIA NIH HHS
• R56 AG020098 NIA NIH HHS
• HD050735 NICHD NIH HHS
• EB008432 NIBIB NIH HHS
• R01 EB008281-14 NIBIB NIH HHS
• R01 AG020098-09 NIA NIH HHS
• R01 EB008281 NIBIB NIH HHS
• R01 EB007813-04 NIBIB NIH HHS
• R01 HD050735 NICHD NIH HHS
• R01 EB008432 NIBIB NIH HHS
• EB008281 NIBIB NIH HHS
• R01 AG020098 NIA NIH HHS
• R01 EB008432-03 NIBIB NIH HHS

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Effects of image noise in muscle diffusion tensor (DT)-MRI assessed using numerical simulations

Diffusion tensor (DT)-MRI studies of skeletal muscle provide information about muscle architecture, microstructure, and damage. However, the effects of noise, the diffusion weighting (b)-value, and partial volume artifacts on the estimation of the diffusion tensor (D) are unknown. This study investigated these issues using Monte Carlo simulations of 3 x 9 voxel regions of interest (ROIs) containing muscle, adipose tissue, and intermediate degrees of muscle volume fractions (f(M)). A total of 1000 simulations were performed for each of eight b-values and 11 SNR levels. The dependencies of the eigenvalues (lambda(1-3)), mean diffusivity (lambda), and fractional anisotropy (FA), and the angular deviation of the first eigenvector from its true value (alpha) were observed. For moderate b-values (b = 435-725 s/mm(2)) and f(M) = 1, an accuracy of 5% was obtained for lambda(1-3), lambda, and FA with an SNR of 25. An accuracy of 1% was obtained for lambda(1-3), lambda, and FA with f(M) = 1 and SNR = 50. For regions with f(M) = 8/9, 5% accuracy was obtained with SNR = 40. For alpha, SNRs of >or=25 and >or=45 were required for +/-4.5 degrees uncertainty with f(M) = 1 and f(M) = 0.5, respectively; SNR >or= 60 was required for +/-9 degrees uncertainty in single muscle voxels. These findings may influence the design and interpretation of DT-MRI studies of muscle microstructure, damage, and architecture.

Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable time

Our objective was to develop a diffusion tensor MR imaging pulse sequence that allows whole brain coverage with isotropic resolution within a clinically acceptable time. A single-shot, cardiac-gated MR pulse sequence, optimized for measuring the diffusion tensor in human brain, was developed to provide whole-brain coverage with isotropic (2.5 x 2.5 x 2.5 mm) spatial resolution, within a total imaging time of approximately 15 min. The diffusion tensor was computed for each voxel in the whole volume and the data processed for visualization in three orthogonal planes. Anisotropy data were further visualized using a maximum-intensity projection algorithm. Finally, reconstruction of fiber-tract trajectories i.e., "tractography" was performed. Images obtained with this pulse sequence provide clear delineation of individual white matter tracts, from the most superior cortical regions down to the cerebellum and brain stem. Because the data are acquired with isotropic resolution, they can be reformatted in any plane and the sequence can therefore be used, in general, for macroscopic neurological or psychiatric neuroimaging investigations. The 3D visualization afforded by maximum intensity projection imaging and tractography provided easy visualization of individual white matter fasciculi, which may be important sites of neuropathological degeneration or abnormal brain development. This study has shown that it is possible to obtain robust, high quality diffusion tensor MR data at 1.5 Tesla with isotropic resolution (2.5 x 2.5 x 2.5 mm) from the whole brain within a sufficiently short imaging time that it may be incorporated into clinical imaging protocols.